0001.tex

\begin{exerciseStatement}


 Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. 

\[ -{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em}
      x( 5 )= -1 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[(-\infty,+\infty)\]
\end{exerciseAnswer}